Mission to Mars

MAE 598: Design Optimization Final Project By: Trevor Slawson, Jenna Lynch, Adrian Maranon, and Matt Catlett

Motivation

• Manned missions beyond low Earth orbit have

not occurred since Apollo 17 (1972).

• Astronomical objects outside the Earth’s sphere

of influence are prime for exploration.

• NASA has plans for a mission to Mars, but the

tentative date is somewhere in 2030.

• Increasingly ambitious rover missions suggest

that the logistics of a human mission may be

possible even sooner.

Basic Rocket Science

• Rocket propulsion is achieved by burning energetic fuel

mixtures and expelling the exhaust in the opposite direction:

• Unfortunately for us (and NASA), things can get much more

complicated from there.

NASA Exploration Page (Grades 9-10): http://exploration.grc.nasa.gov/education/rocket/rockth.html

Less Basic Rocket Science

• During atmospheric flight, several

forces are active all at once:

– Thrust

– Weight

– Lift

– Drag

• During orbital maneuvering, the

calculations are dependent only on

propulsion forces (no atmosphere):

– Thrust

• For now, focus on the orbital part

NASA Exploration Page (Grades 10-12): http://exploration.grc.nasa.gov/education/rocket/rktth1.html

Orbital Maneuvering

• In orbit, change in altitude is proportional to change in speed.

• When orbital maneuvering is performed, the motion of a rocket can

be described by the Tsiolkovsky rocket equation:

Δ𝑣 = 𝑣𝑒 ln𝑚0

𝑚1

• The exhaust velocity (𝑣𝑒 ) and the ratio of masses returns the

maximum change in speed, referred to simply as delta-v (Δ𝑣).

• Fortunately this model can also be applied to non-orbital

maneuvers via the concept of delta-v budget.

• Unfortunately, the fuel required to move a certain payload mass

increases exponentially (Tyranny of the Rocket Equation).

Approach

Four-step plan:

1. Launch the payload and some

fuel into LEO

2. Launch extra fuel and astronauts

into LEO

3. Dock the two halves together,

then fly to Mars

4. Land on the Martian surface

Goal:

Oppose the tyranny of the rocket

equation and get as many people on

Mars as possible!

Approach

Four-step plan:

1. Launch the payload and some

fuel into LEO

2. Launch extra fuel and astronauts

into LEO

3. Dock the two halves together,

then fly to Mars

4. Land on the Martian surface

Goal:

Oppose the tyranny of the rocket

equation and get as many people on

Mars as possible!

Approach

Four -step plan:

1. Launch the payload and some

fuel into LEO

2. Launch extra fuel and astronauts

into LEO

3. Dock the two halves together,

then fly to Mars

4. Land on the Martian surface

Goal:

Oppose the tyranny of the rocket

equation and get as many people on

Mars as possible!

Approach

Four -step plan:

1. Launch the payload and some

fuel into LEO

2. Launch extra fuel and astronauts

into LEO

3. Dock the two halves together,

then fly to Mars

4. Land on the Martian surface

Goal:

Oppose the tyranny of the rocket

equation and get as many people on

Mars as possible!

Proactive Supply Launch

(PSL)

The astronauts on Mars

will inevitably be faced

with equipment failures.

This launch plan will

ensure that replacement

gear is delivered in an

optimal way.

Interplanetary Vehicle

(IPV)

The IPV is the vehicle

that will make the trip

from LEO to Mars. It is

made up of two halves

(one being the payload)

that are launched into

LEO atop the OLB.

Orbital Launch Booster

(OLB)

The OLB is a three stage

rocket launch system

similar to the Saturn V

Rocket that will be used

to get the IPV halves

into low earth orbit.

Subsystem Overview

Proactive Supply Launch

Objective: Minimize the

number of supply

launches needed.

Trades:

• Few launches means

bigger payloads

• Launches are very

expensive

Interplanetary Vehicle

Objective: Maximize the

number of astronauts

who can be sent in 1 trip

Trades:

• Less astronauts are

easier to send

• More people means

more sustainability

Orbital Launch Booster

Objective: Minimize the

OLB mass while still

achieving LEO

Trades:

• Lighter rockets are

cheaper

• Heavier rockets can

lift a bigger IPV

Objectives and Tradeoffs

• A delta-v of roughly 18 km/s is required to land softly on Mars, therefore

mass is a consideration in the tradeoff for every subsystem.

IPV Subsystem

• System Objective: Maximize the

number of astronauts

• Assumptions:

1. The trip will take 9 months

2. The IPV will carry 4000 kg of gear

3. 89% of food mass is lost during the trip

4. The IPV will stage during both burns

5. LEO to TMI delta-v is 4.6 km/s

6. TMI to Soft-Land delta-v is 5.6 km/s

7. Aerobraking and parachutes are used

to assist with the soft landing

Variables

• Radius

• Height of each section

• Fuel Remainder Ratio (Amount

of fuel in each half of the IPV)

• Number of Astronauts

Constraints

• Delta-v requirements

• Food/water per person

• 3 Stages

• Each half of the IPV has the

same mass

Outputs

• Payload Mass and Volume

• IPV Mass and Dimensions

Crew Space

Equipment

Food/Water

Fuel

Jumpseat

Fuel

IPV-1 IPV-2

IPV Subsystem

• Subsystem Verification: Feasibility

was checked with the Saturn V

payload limit (118 metric tons) as

a constraint.

• Results: An IPV with capacity for 3

astronauts will meet all of the

requirements and has the

following dimensions:

– Overall Radius: 2 m

– Overall Height: 22.6 m

– IPV-1 Mass: 112 metric tons

– IPV-2 Mass: 112 metric tons

IPV-2

IPV-1

Lander

Equipment/

Consumables

Crew Living

Space

Fuel

Crew

Jumpseat

OLB Subsystem

• System Objective: Minimize the

mass of the booster stages.

• Assumptions:

1. The IPV is the maximum mass lift

requirement.

2. Delta-v budget simplifications are valid

in the atmosphere

3. Earth to LEO delta-v is 9.0 km/s

4. All performance characteristics are

identical to those of the Saturn V

5. Structural mass is based on the

surface area of each stage

Variables

• Radius of each stage

• Height of each stage

• Number of engines per stage

(Predetermined types)

Constraints

• Delta-v requirements

• Burn time less than 800 sec

• Can lift the IPV halves to LEO

• Thrust-to-weight ratio at stage

start is greater than 1

• Acceleration at stage end is

less than 6 g

• Radius of stage n must be less

than or equal to that of n-1

Outputs

• (Determines Feasibility)

OLB, Stage n

MAR

S O

R B

UST

OLB Subsystem

• Subsystem Verification: Feasibility

was checked with the Saturn V

payload limit (118 metric tons) as

a constraint. The number of

engines was fixed at [5,5,1].

• Results: An OLB with roughly the

same parameters as the Saturn V

was the optimal solution!

PSL Subsystem

• System Objective: Minimize the number

of launches required to sustain the

astronauts.

• Assumptions:

1. The PSL subsystem consists of analyzing supply

launches. The launches will be unmanned.

2. The subsystem uses the mass and volume

values generated in IPV subsystem.

3. Lifetime = MTBF for each assembly.

4. 75 subassembly components simplified to 7

major assemblies.

5. Launches will be scheduled yearly.

6. It is assumed that it takes 1 year to get to Mars.

7. Assemblies come from Mars One mission plan.

• Results: See optimal system results.

Variables

• Oxygen Generation Assembly

• Carbon Dioxide Removal Assembly

• Common Cabin Air Assembly

• Urine Processor Assembly

• Water Processor Assembly

• CO2 Reduction Assembly

• In-Situ Resource Utilization (ISRU)

Constraints

• Mass (9770 kg)

• Volume (79.87 m^3)

• Mean Time Between Failures (MTBF)

Outputs

• Number & time of launches

Mass

Constraint

Mass

Constraint IPV

System Design Flowchart

• System Objective: Maximize the number of astronauts that can be sent to

the surface of Mars and then sustained thereafter for a period of 22 years.

• Interactions: The systems will solve iteratively as shown, starting with the

IPV and ending with a feasible PSL.

OLB PSL

Volumetric

Constraint

Feasibility Revision

(As Needed)

Optimization Challenges

Subsystem Interdependence

• Challenge: It was not possible to

optimize the IPV, OLB, and PLS

simultaneously due to their

interdependence.

• Solution: Solve the IPV subsystem

first (most critical), then optimize

the OLB, and finally the PSL.

Integer Variables

• Challenge: Many variables had to

be integer values for the results to

make sense.

– OLB: Number of engines per stage

– PSL: Number of replacement

systems per launch

• OLB Solution: Treat the integer

variables as parameters and solve

each of the cases independently

with loops (432 cases in < 5 min).

• PSL Solution: Too many variables

to check all cases with loops.

Instead, use genetic algorithm.

System Results - IPV

• Amount of astronauts was

varied from 1 to 4 and

each case was solved

independently.

• No failure is observed at

this level because this

subsystem is constrained

by the OLB.

• Greater than 4 astronauts

required excessive amount

of weight and did not

initially seem feasible.

• IPV complete, proceed to

the OLB optimization.

Parameter IPV Case

Astronauts

(#) 1 2 3 4

Radius

(m) 2.0 2.0 2.0 2.0

Height

(m) 19.3 21.0 22.6 24.3

Volume

(m³) 75.5 77.7 79.8 82.1

Payload

(metric ton) 7.4 8.6 9.7 10.9

Half-Mass

(metric ton) 90 101 112 123

Larger than Saturn V – Less Feasible

System Results - OLB

• Optimal solution was

found for each number of

astronauts. Geometry in

comparison with the

Saturn V is shown for each

case.

• First signs of failure are

observed; a crew of four

astronauts cannot be sent

in a single trip.

– Eliminates the less feasible

result from IPV optimization.

• New optimal solution of 3

astronauts (as per the

objective function)

Saturn V (in blue) compared with the

OLB’s for n=[1,2,3] astronauts

n=1 n=2 n=3

Parameter Optimal OLB Saturn V

Height (m) 98 92

GVW (metric tons) 3644 2909

Engines/Stage [6,6,3] [5,5,1]

• Optimal launch plan for 3 astronauts was found using the IPV and OLB

combination results.

System Results - PSL

• An optimized resupply plan of only

15 launches will meet the needs

of the crew over a period of 22

years without any equipment

downtime.

– Maximum Mass: 1021 kg

– Maximum Volume: 2.4 m³

• IPV, OLB, and PLS are all

optimized at this point.

• Since the maximum mass and

volume are so low, the scope of

the project could be expanded.

– More astronauts over time

– Larger bases (population growth)

– Smaller teams (more exploration)

System Results – PSL

Orbital Launch Booster

Each half of the IPV will

be lifted into orbit by the

largest rocket ever built.

With a mass 25% larger

than that of the Saturn

V, the OLB could put a

third of the mass of the

ISS into low earth orbit

with a single launch.

Interplanetary Vehicle

A two-part vehicle with

95% fuel by mass will

ferry three astronauts

from LEO to Mars in a

trip that will last nearly 9

months. They land next

to an automated supply

ship and set up a small

colony when they arrive.

Proactive Supply Launch

Each year replacement

equipment is sent on

automated IPV’s. Vital

systems are replaced

before they fail, allowing

the colony to survive for

the estimated 22 years

required for them to

achieve self-sufficiency.

Overall Results

Questions?

Appendix 1 – OLB Model

Variables:

𝑠 = [1,2,3] ≡ 𝑠𝑡𝑎𝑔𝑒 𝑛𝑢𝑚𝑏𝑒𝑟 ℎ𝑠 ≡ ℎ𝑒𝑖𝑔ℎ𝑡 𝑜𝑓 𝑠𝑡𝑎𝑔𝑒 𝑠

𝑟𝑠 ≡ 𝑟𝑎𝑑𝑖𝑢𝑠 𝑜𝑓 𝑠𝑡𝑎𝑔𝑒 𝑠

𝑛𝑠 ≡ 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑠𝑡𝑎𝑔𝑒 𝑠 𝑡ℎ𝑟𝑢𝑠𝑡𝑒𝑟𝑠

Appendix 2 – IPV Model

Appendix 3 – PSL Model Mass (kg) Vol (m^3) MTBF (years)

Oxygen Generation Assembly 223.13 0.2542 5.419977169

Carbon Dioxide Removal 156.32 0.4239 3.755707763

Common Cabin Air Assembly 100.91 0.6097 3.755707763

Urine Processor Assemlby 244.67 0.4837 3.12

Water Processor Assembly 620.85 0.7537 2.92

CO2 Reduction Assembly 219.49 0.6812 5.707762557

ISRU 220.82 1.1986 7.610353881 Table 1: Assemblies and their respective mass, volume, and MTBF.

Table 2: Number of assemblies per launch. Highlighted launches are empty launches.